In a nutshell:
Most single-family residence are FHA eligible, but it is up to the seller if they will accept an offer using an FHA loan. Typically this just depends on the types of offers they receive (i.e. if they receive an all-cash offer they would most likely choose that over an FHA due to the quicker close).
In addition, it's a good idea to check with your lender and provide them with the specific address of the property you are interested in(especially for any single family residences [SFRs]), to ensure they are able to issue the loan on the specific property.
When looking for apartments, townhomes, and condos, it is possible that the complex has been pre-approved by the FHA. Here’s a link to the HUD website where you can look up buildings to see if they’re FHA approved.